Introduction to Financial Management

Preferred stock is called a hybrid security because it combines features of both debt (bonds) and equity (common stock).

• Equity features: It represents ownership in the company, holders receive dividends (not interest), dividends are paid out of profit after tax, and it has no fixed maturity date.
• Debt features: It carries a fixed rate of dividend, has a stated par value, ranks ahead of common stock in payment of dividends and in claims on assets at liquidation, and usually has no voting rights.

Since it possesses characteristics of both debt and equity, preferred stock is known as a hybrid (or quasi-debt) security.

Given: $r^*$ = 2%; inflation = 3%, 3.5%, 4% in years 1, 2, 3; $MRP = 0.1(t-1)\%$; LP (3-year) = 0.25%; DRP (3-year) = 0.6%.

Yield = $r^* + IP + MRP\,(+\,LP + DRP$ for corporate bonds$)$

(a) 1-year T-bill

$IP = 3\%$, $MRP = 0.1(1-1) = 0\%$

$r = 2\% + 3\% + 0\% = \mathbf{5\%}$

(b) 3-year T-bond

Average inflation: $IP = \dfrac{3+3.5+4}{3} = 3.5\%$; $MRP = 0.1(3-1) = 0.2\%$

$r = 2\% + 3.5\% + 0.2\% = \mathbf{5.7\%}$

(c) 3-year corporate bond

Add the default risk premium and liquidity premium to the T-bond yield:

$r = 5.7\% + 0.6\% + 0.25\% = \mathbf{6.55\%}$

The yield rises with maturity (5% to 5.7%) because of higher expected inflation and the maturity risk premium, and the corporate bond pays 0.85% more than the T-bond as compensation for default and liquidity risk.

(a) Average inflation over 3 years

$\frac{3\% + 3.5\% + 4.5\%}{3} = \frac{11\%}{3} = 3.67\%$

(b) Yield on a 1-year T-bill

A T-bill has no default, liquidity or maturity risk premium (assumed zero for one year), so it is the real rate plus the expected inflation of year 1:

$r = 2\% + 3\% = 5\%$

(c) Yield on a 3-year corporate bond

$r = r^* + IP + MRP + LP + DRP = 2\% + 3.67\% + 0.40\% + 0.30\% + 0.60\% = 6.97\%$

The 3-year corporate bond yields about 6.97%.

Finance is the branch of management that deals with the planning, raising, allocating, and controlling of monetary resources (funds) of an individual, business, or government in order to achieve desired objectives at minimum cost and risk.

In simple terms, finance means the management of money — how funds are obtained (financing decision), how they are invested (investment decision), and how the returns earned are distributed (dividend decision). It bridges the gap between the sources of funds and their effective utilisation.

Four examples of financial instruments:

1. Shares (equity securities) — e.g., ordinary shares of a listed company.
2. Bonds and debentures — e.g., government bonds, corporate debentures.
3. Treasury bills — short-term money market instruments issued by the central bank.
4. Derivatives — e.g., futures, options, and forward contracts.

The four major functions of finance are:

1. Investment (financing) decision – Deciding in which long-term assets and projects the firm should invest its funds, so as to earn the highest possible return.
2. Financing decision – Determining the best mix of debt and equity (capital structure) to raise the funds needed for investment.
3. Dividend decision – Deciding how much of the profit should be distributed to shareholders as dividends and how much should be retained for reinvestment.
4. Liquidity (working capital) management – Managing current assets and current liabilities to ensure the firm can meet its short-term obligations without holding excessive idle funds.

Yield to Maturity (YTM) is the total return an investor earns if a bond is held until its maturity date, assuming all coupon payments are reinvested at the same rate. It is calculated using the bond's maturity period (n) and face value received at maturity.

Yield to Call (YTC) is the total return an investor earns if a callable bond is redeemed by the issuer before maturity, on the call date. It is calculated using the call period and the call price instead of the maturity period and face value.

In short, YTM assumes the bond runs its full life, while YTC assumes the issuer calls it early. For a callable bond selling at a premium, YTC is normally lower than YTM.

Working capital management is the process of managing a firm's short-term assets (current assets such as cash, marketable securities, accounts receivable and inventory) and short-term liabilities (current liabilities such as accounts payable and short-term loans) in order to maintain a balance between profitability and liquidity.

In simple terms, it involves deciding how much to invest in current assets and how to finance that investment so that the firm can meet its day-to-day operating expenses and short-term obligations without holding excessive idle funds.

Compare both amounts at the same point in time by finding the present value of Rs 1500 received after 5 years.

$PV = \frac{1500}{(1.10)^5} = \frac{1500}{1.61051} \approx \text{Rs } 931.39$

Since Rs 931.39 < Rs 1,000, Rs 1,000 in hand today is worth more than Rs 1,500 after 5 years at 10%.

Given: par value = Rs 100, dividend rate = 10%, required yield $k_p$ = 8%.

Annual preferred dividend: $D_p = 10\% \times 100 = \text{Rs } 10$

For a perpetual preferred stock:

$V_p = \frac{D_p}{k_p} = \frac{10}{0.08} = \text{Rs } 125$

The value of the stock is Rs 125, which is above par because the dividend yield demanded by the market (8%) is lower than the stated dividend rate (10%).

Given:

• Expected dividend at the end of the year, (D_1 = \text{Rs } 12)
• Required rate of return, (r_s = 11% = 0.11)
• Growth rate, (g = 5% = 0.05)

Formula (Gordon's constant growth model):

$P_0 = \frac{D_1}{r_s - g}$

Substitution:

$P_0 = \frac{12}{0.11 - 0.05} = \frac{12}{0.06}$

$P_0 = \text{Rs } 200$

Answer: The stock's price would be Rs 200.

Given: loan $PV$ = Rs 200,000, $i$ = 12%, $n$ = 5 years.

$A = PV \times \frac{i}{1-(1+i)^{-n}} = 200{,}000 \times \frac{0.12}{1-(1.12)^{-5}}$

Since $(1.12)^5 = 1.76234$, $(1.12)^{-5} = 0.56743$.

$A = 200{,}000 \times \frac{0.12}{0.43257} = 200{,}000 \times 0.27741 \approx \text{Rs } 55{,}482$

The annual installment is about Rs 55,482.

Relationship between Economics, Finance and Accounting

Economics, finance and accounting are three closely related but distinct disciplines that together support business decision-making. Their relationship can be explained as follows:

1. Economics as the foundation: Economics studies how scarce resources are allocated to satisfy unlimited wants. It provides the theoretical base — concepts like demand, supply, cost, profit, inflation, interest rate and national income — on which both finance and accounting depend. Business decisions such as pricing, output level and investment are guided by economic principles (micro and macro).

2. Finance as the application of economic principles to funds: Finance deals with raising, allocating and managing funds to maximise the wealth of owners. It uses economic tools (time value of money, risk–return trade-off, cost of capital) to decide where to invest and how to finance assets. Thus finance is often called applied economics.

3. Accounting as the language and information base: Accounting records, classifies and summarises business transactions and communicates the results through financial statements. It supplies the data (income, expenses, assets, liabilities, cash flows) that finance needs for analysis and that economics needs for measurement and forecasting.

4. Interdependence:

• Accounting provides the figures; finance interprets them for investment, financing and dividend decisions.
• Finance supplies the economic logic (cost, return, risk) for judging those figures.
• Economics provides the environment (interest rate, tax policy, market structure) within which both operate.

5. Distinction in focus:

Conclusion: Economics gives the theory, finance applies it to fund management, and accounting provides the reliable financial information on which both depend. They are complementary — none can function effectively in business without the other two.

Financial Market

A financial market is a market in which financial assets (securities) such as stocks, bonds, bills, and other instruments are bought and sold, and where funds are transferred from those who have surplus funds (savers/lenders) to those who need funds (borrowers/investors). It provides the mechanism through which the financial system channels savings into productive investment. Its main functions are to mobilise savings, allocate credit efficiently, provide liquidity to investors, determine prices of financial assets, and reduce the cost of transactions between surplus and deficit units. Financial markets are broadly classified into the money market (short-term funds) and the capital market (long-term funds).

Distinction between Money Market and Capital Market

Conclusion: The money market meets short-term liquidity needs, while the capital market supplies long-term capital for investment. Both are complementary parts of the financial system — the money market keeps the system liquid, and the capital market drives long-term economic growth.

Cost of money is the rate of return (interest rate) that investors demand for lending their funds, or equivalently the price a borrower must pay to use someone else's money for a period of time. It is the required rate of return that equates the supply of and demand for loanable funds in the financial markets. In finance, the cost of money is the base interest rate on a risk-free security, on which all other interest rates are built.

Four fundamental factors affecting the cost of money:

1. Production opportunities — The investment opportunities available in an economy to put the borrowed funds to productive use. The more profitable the available investment projects (their expected returns), the greater the demand for funds, and hence the higher the cost of money. A growing economy with many profitable projects pushes interest rates up.

2. Time preferences for consumption — The preference of savers (consumers) for current consumption versus future consumption. If people strongly prefer to spend now rather than save, they must be induced to save by a higher interest rate, which raises the cost of money. A society that is more willing to defer consumption will supply more funds and lower the cost of money.

3. Risk — The uncertainty about the return on an investment. The greater the perceived risk that the borrower may default or that returns may fall short of expectations, the higher the return investors demand as compensation. Thus, higher risk increases the cost of money.

4. Inflation — The expected rate of decline in the purchasing power of money. Investors demand a return high enough to preserve their real purchasing power, so expected inflation is added to the required return. Higher expected inflation therefore raises the cost of money.

These four factors together determine the supply of and demand for loanable funds, and hence the general level of interest rates in the economy.

Time value of money (TVM) is the principle that a rupee received today is worth more than the same rupee received in the future, because money available now can be invested and earn a return. Its importance in finance is as follows:

1. Valuation of assets and securities. TVM provides the basis for valuing bonds, shares, and any asset whose returns are spread over time. Future cash flows are discounted to their present value to determine what the asset is worth today.

2. Capital budgeting decisions. Long-term investment projects are appraised using discounted techniques such as Net Present Value (NPV), Internal Rate of Return (IRR) and Profitability Index. These techniques compare the present value of future benefits with the present cost of investment, so that only wealth-creating projects are accepted.

3. Cost of capital and financing decisions. The cost of debt, preference shares and equity is computed by discounting the future payments (interest, dividend, redemption value) to their present value. This helps in choosing the cheapest and most suitable mix of financing.

4. Comparison of alternative investment options. Cash flows occurring at different points of time cannot be compared directly. TVM converts them to a common present or future value, making rational comparison possible.

5. Working capital and cash management. It guides decisions on credit policy, cash discounts, inventory levels and holding of cash balances, since early recovery of cash and early payment of obligations have measurable financial value.

6. Loan, lease and insurance decisions. The equated instalments of loans, lease rentals, sinking fund deposits and annuity values are all computed using TVM concepts, enabling borrowers and lenders to evaluate the real cost and return.

7. Personal and corporate financial planning. It helps in planning savings, retirement funds, education funds and dividend policy by showing how much must be set aside today to reach a target amount in the future.

In short, TVM is the foundation of financial decision-making: it makes cash flows occurring at different times comparable, and thereby supports sound investment, financing and dividend decisions aimed at maximising shareholder wealth.

Given: $D_0$ = Rs 20, $g$ = 5% for 3 years, $r$ = 12%, holding period = 3 years.

(a) Expected dividend stream

• $D_1 = 20(1.05) = \text{Rs } 21.00$
• $D_2 = 21(1.05) = \text{Rs } 22.05$
• $D_3 = 22.05(1.05) = \text{Rs } 23.1525$

(b) Current stock price

The price at the end of year 3 is the present value of the dividends after that, which also grow at 5%:

$D_4 = 23.1525(1.05) = 24.3101, \qquad P_3 = \frac{D_4}{r-g} = \frac{24.3101}{0.12-0.05} = \text{Rs } 347.29$

$P_0 = \frac{21.00}{1.12} + \frac{22.05}{(1.12)^2} + \frac{23.1525}{(1.12)^3} + \frac{347.29}{(1.12)^3}$

$P_0 = 18.75 + 17.58 + 16.48 + 247.19 \approx \text{Rs } 300$

The current stock price is about Rs 300.

a. Weighted Average Cost of Capital (WACC)

Given:

• Weight of common stock, $w_e$ = 70% = 0.70
• Weight of preferred stock, $w_p$ = 5% = 0.05
• Weight of debt, $w_d$ = 25% = 0.25
• Cost of equity, $r_e$ = 11%
• Cost of preferred stock, $r_p$ = 5%
• Pretax cost of debt, $r_d$ = 7%
• Tax rate, $T$ = 40%

Formula:

$WACC = w_e r_e + w_p r_p + w_d r_d(1 - T)$

Substitution:

$WACC = (0.70)(0.11) + (0.05)(0.05) + (0.25)(0.07)(1 - 0.40)$

$WACC = 0.077 + 0.0025 + (0.25)(0.07)(0.60)$

$WACC = 0.077 + 0.0025 + 0.0105$

$WACC = 0.0900 = 9.00\%$

Result: The company's WACC is 9.00 percent.

b. Advice to the President

The president's reasoning is based on comparing the stated (pretax) costs of preferred stock (5%) and debt (7%). This comparison is misleading for two reasons:

1. Interest on debt is tax-deductible, but preferred dividends are not. The relevant cost of debt is the after-tax cost:

$r_d(1 - T) = 7\%(1 - 0.40) = 4.20\%$

Since 4.20% is lower than the 5% cost of preferred stock, debt is actually the cheaper source of financing on an after-tax basis. Preferred dividends are paid out of after-tax income, so no such tax shield exists for preferred stock.

2. Risk and financial distress costs. Even ignoring taxes, increasing preferred stock (or any senior security) raises the firm's fixed financial obligations. Greater use of preferred stock increases financial risk, which raises the cost of both debt and equity, and raises the possibility of financial distress and bankruptcy costs. These costs would offset any apparent saving from a lower stated cost.

3. Loss of financial flexibility. Preferred stock carries fixed dividend obligations that must be met before common dividends. Issuing too much preferred stock reduces the firm's retained earnings cushion and its ability to absorb losses, limiting future financing flexibility.

Conclusion: The firm should not shift toward more preferred stock financing merely because its stated cost appears lower. On an after-tax, risk-adjusted basis, debt remains the cheapest source of capital, and the current target structure of 70% equity, 5% preferred, and 25% debt should be maintained unless it can be shown that a change reduces the overall WACC without materially increasing financial risk.

Given:

• Annual sales = Rs 12,000,000
• Cost of goods sold (COGS) = Rs 9,000,000
• Inventory = Rs 3,000,000
• Accounts receivable (AR) = Rs 3,250,000
• Accounts payable (AP) = Rs 1,250,000
• Days in a year = 365

Formulae: [ \text{Inventory conversion period (ICP)} = \frac{365}{\text{Inventory turnover}} = \frac{365 \times \text{Inventory}}{\text{COGS}} ] [ \text{Receivables collection period (RCP)} = \frac{365 \times \text{AR}}{\text{Sales}} ] [ \text{Payables deferral period (PDP)} = \frac{365 \times \text{AP}}{\text{COGS}} ] [ \text{Cash conversion period (CCP)} = \text{ICP} + \text{RCP} - \text{PDP} ]

Calculation: [ \text{ICP} = \frac{365 \times 3,000,000}{9,000,000} = 121.67 \text{ days} ] [ \text{RCP} = \frac{365 \times 3,250,000}{12,000,000} = 98.85 \text{ days} ] [ \text{PDP} = \frac{365 \times 1,250,000}{9,000,000} = 50.69 \text{ days} ] [ \text{CCP} = 121.67 + 98.85 - 50.69 = 169.83 \text{ days} ]

Result: The cash conversion period of Dabur Nepal is approximately 170 days. This means the company takes about 170 days to convert its inventory and receivables into cash after accounting for the time it takes to pay its suppliers.

Cost of Capital

Cost of capital is the minimum rate of return that a firm must earn on its investments to maintain the market value of its shares and satisfy its investors (lenders and shareholders). It is the required rate of return used as the discount rate in capital budgeting and as the hurdle rate for accepting or rejecting projects. It represents the weighted average cost of the various long-term sources of funds — debt, preference shares, equity shares and retained earnings — and is therefore also called the weighted average cost of capital (WACC).

$\text{WACC} = W_d K_d(1-t) + W_p K_p + W_e K_e + W_r K_r$

where $W$ = proportion of each source in the capital structure and $K$ = cost of each source.

Factors Affecting the Cost of Capital

1. General economic conditions Interest rates, inflation and the state of the economy directly influence the cost of capital. During inflation or tight money policy, interest rates rise, so the cost of debt and equity both increase. In a recession, investors demand a higher risk premium, raising the cost of capital.

2. Market conditions (demand and supply of funds) When the supply of savings is low relative to demand for investment funds, the cost of capital rises. A bullish or bearish securities market also affects the price at which new shares can be issued, and hence the cost of equity.

3. Business risk Firms with unstable sales, high operating leverage or volatile earnings are considered risky. Investors demand a higher return to compensate for this risk, which increases the cost of equity and debt.

4. Financial risk (capital structure policy) The greater the use of debt in the capital structure, the higher the financial risk borne by shareholders. This raises the cost of equity. However, debt is cheaper due to the tax shield on interest, so a moderate use of debt can lower the WACC; excessive debt raises it.

5. Tax rate Interest on debt is a tax-deductible expense. A higher corporate tax rate reduces the effective cost of debt, $K_d(1-t)$, and thus lowers the overall cost of capital. Dividends are not tax-deductible, so the cost of equity is unaffected by the tax rate in this way.

6. Dividend policy A firm that retains a large portion of earnings avoids flotation costs on new equity, so retained earnings are cheaper than fresh equity. A policy of high dividend payout forces the firm to raise costly external equity, raising the overall cost of capital.

7. Floatation costs Costs of issuing new securities (underwriting, brokerage, registration) increase the effective cost of new debt and equity. The higher the flotation cost, the higher the cost of external financing.

8. Firm's creditworthiness and size Large, well-established firms with good credit ratings can borrow at lower interest rates and issue securities cheaply. Small or newly established firms face higher risk and must pay a higher cost of capital.

9. Growth and stability of earnings A firm with stable and growing earnings is viewed as less risky; investors accept a lower return. Unstable earnings raise the required return and hence the cost of capital.

10. Level of interest rates and monetary policy Central bank policy (e.g., bank rate, CRR, open market operations) changes the cost of borrowing in the economy. A tight monetary policy raises interest rates and the cost of capital.

11. Capital structure mix The relative proportion of debt and equity in the total capital determines the WACC. An optimal mix minimizes the cost of capital; a sub-optimal mix raises it.

Conclusion The cost of capital is the firm's required rate of return and the key link between financing and investment decisions. It is not fixed — it changes with economic conditions, risk, tax policy, dividend policy and the firm's capital structure. Management should aim for an optimal capital structure and sound financial policies to keep the cost of capital as low as possible.

Given:
(FV = \text{Rs } 1000)
Annual interest rate (i = 8% = 0.08)
Need amount on January 1, 2021.

a. Deposit on January 1, 2018 with annual compounding

Time from Jan 1, 2018 to Jan 1, 2021 = 3 years.

[ PV=\frac{FV}{(1+i)^n} ]

[ PV=\frac{1000}{(1.08)^3} =\frac{1000}{1.259712} =\text{Rs } 793.83 ]

Answer: Rs 793.83

b. Deposit on January 1, 2018 with semi-annual compounding

Semi-annual rate:

[ \frac{i}{m}=\frac{0.08}{2}=0.04 ]

Number of periods:

[ n=3 \times 2=6 ]

[ PV=\frac{1000}{(1.04)^6} =\frac{1000}{1.265319} =\text{Rs } 790.31 ]

Answer: Rs 790.31

c. Four equal payments on January 1, 2018, 2019, 2020 and 2021

Let each payment be (A).

The first payment earns interest for 3 years, the second for 2 years, the third for 1 year, and the fourth for 0 years.

[ A(1.08)^3 + A(1.08)^2 + A(1.08)^1 + A = 1000 ]

[ A[1.259712 + 1.1664 + 1.08 + 1] = 1000 ]

[ A(4.506112)=1000 ]

[ A=\frac{1000}{4.506112} =\text{Rs } 221.92 ]

Answer: Rs 221.92 each year

d. Interest rate required if only Rs 750 is available on January 1, 2018

[ 750(1+r)^3=1000 ]

[ (1+r)^3=\frac{1000}{750}=1.333333 ]

[ 1+r=(1.333333)^{1/3}=1.100642 ]

[ r=0.100642=10.0642% ]

Answer: Approximately 10.06% compounded annually

Final Answers

Given: $M$ = Rs 1,000, coupon = 11% so $INT$ = Rs 110, price = Rs 1,175, $n$ = 10 years, call price = Rs 1,090 after 5 years.

(a) Yield to maturity

$1{,}175 = 110 \times PVIFA_{k,10} + 1{,}000 \times PVIF_{k,10}$

• At 8%: $110(6.7101) + 1000(0.4632) = 1{,}201.31$
• At 9%: $110(6.4177) + 1000(0.4224) = 1{,}128.35$

Interpolating: $k = 8\% + \dfrac{1{,}201.31-1{,}175}{1{,}201.31-1{,}128.35} = 8\% + \dfrac{26.31}{72.96} \approx$ 8.36%

(b) Yield to call

$1{,}175 = 110 \times PVIFA_{k,5} + 1{,}090 \times PVIF_{k,5}$

• At 8%: $110(3.9927) + 1090(0.6806) = 1{,}181.05$
• At 9%: $110(3.8897) + 1090(0.6499) = 1{,}136.26$

Interpolating: $k = 8\% + \dfrac{6.05}{44.79} \approx$ 8.14%

(c) Which yield to expect

Investors should expect to earn the YTC of about 8.14%. The bond sells at a premium (Rs 1,175) because its 11% coupon is well above current market yields, so the company can profitably call it and refinance at a lower rate. Since the YTC is below the YTM, the call is the more likely outcome and the lower yield is the more realistic expectation.

(a) Liquidity ratios (2022)

$\text{Current ratio} = \frac{1{,}290{,}000}{540{,}200} = 2.39\times$

$\text{Quick ratio} = \frac{1{,}290{,}000-836{,}000}{540{,}200} = 0.84\times$

Both ratios are below the industry average, so liquidity is somewhat weak. The quick ratio below 1 shows the firm depends on selling inventory to meet short-term obligations, and inventory is a large share of current assets.

(b) Asset management ratios (2022)

$\text{Inventory turnover} = \frac{3{,}850{,}000}{836{,}000} = 4.61\times$

$DSO = \frac{402{,}000}{3{,}850{,}000/360} = 37.6 \text{ days}$

$\text{Fixed assets turnover} = \frac{3{,}850{,}000}{360{,}800} = 10.67\times$

$\text{Total assets turnover} = \frac{3{,}850{,}000}{1{,}650{,}800} = 2.33\times$

Inventory turns are slow (excess stock) and customers take about 5.6 days longer than average to pay, so receivables and inventory are poorly managed. Fixed assets are used as efficiently as the industry average, but total assets turnover is lower because too much money is tied up in inventory and receivables.

(c) Debt management ratios (2022)

$\text{Debt ratio} = \frac{540{,}200+424{,}612}{1{,}650{,}800} = 58.4\%$

$TIE = \frac{EBIT}{\text{Interest}} = \frac{149{,}700}{76{,}000} = 1.97\times$

$\text{Fixed charge coverage} = \frac{149{,}700+40{,}000}{76{,}000+40{,}000} = 1.64\times$

The firm uses more debt than the industry and earns less cover for its interest and lease payments. Its long-term solvency is therefore weak and risky: a further fall in earnings could make it difficult to service debt, and it will find it hard to raise more loans.

(d) Profitability ratios (2022)

$\text{Net profit margin} = \frac{44{,}220}{3{,}850{,}000} = 1.15\%$

$ROA = \frac{44{,}220}{1{,}650{,}800} = 2.68\%$

$ROE = \frac{44{,}220}{685{,}988} = 6.45\%$

All three are far below the industry. Net income fell from Rs 87,960 in 2021 to Rs 44,220 in 2022 even though sales grew, because other expenses and interest costs rose faster than sales. ROE is helped by high leverage but is still poor.

Overall: The company has weak liquidity, inefficient inventory and receivable management, heavy debt and poor profitability. It needs to control costs, reduce inventory and collect receivables faster, and limit new borrowing.

Business finance is the area of management concerned with raising funds from the best available sources and using them efficiently in the firm's assets, so that the firm's value and the owners' wealth are maximised. It covers investment, financing and dividend decisions.

A primary market is where new securities are issued for the first time by the issuer to investors (IPOs, right issues), and the issuing firm receives the money. A secondary market is where already-issued securities are traded among investors (for example the stock exchange); the issuer receives no funds, but the market gives liquidity and price discovery.

Free cash flow (FCF) is the cash flow available to all investors (creditors and shareholders) after the firm has paid for the operating expenses, taxes and the investment in operating capital needed to sustain operations:

$FCF = NOPAT - \text{Net investment in operating capital}$

It can be paid out as interest, debt repayment, dividends or share repurchases, and it is the basis of firm valuation.

In an ordinary annuity the equal payments are made at the end of each period, whereas in an annuity due they are made at the beginning of each period. Hence an annuity due earns one extra period of interest:

$FVA_{due} = FVA_{ordinary}\times(1+r), \qquad PVA_{due} = PVA_{ordinary}\times(1+r)$

A bond is a long-term debt security in which the issuer (government or company) borrows money from investors and promises to pay a fixed periodic interest (coupon) and to repay the par (face) value at maturity.

The weighted average cost of capital (WACC) is the average cost of the firm's long-term funds, in which the cost of each source (debt, preferred stock, common equity) is weighted by its proportion in the target capital structure:

$WACC = w_d\,k_d(1-T) + w_p\,k_p + w_e\,k_e$

Financial securities are tradable financial assets that represent a claim on the issuer's assets or income, issued to raise funds. They are bought by investors who expect a return, and are traded in the financial markets.

Some financial instruments:

• Treasury bills: short-term (up to 1 year) government securities sold at a discount and redeemed at face value.
• Bonds/debentures: long-term debt securities paying fixed interest and the principal at maturity.
• Preferred stock: hybrid security paying a fixed dividend with priority over common stock.
• Common stock: ownership shares with residual claim on income and assets, and voting rights.
• Certificates of deposit and commercial paper: short-term money market instruments issued by banks and companies.
• Derivatives (options, futures): contracts whose value is derived from an underlying asset.

Expected inflation over the two years averages $(2\% + 4\%)/2 = 3\%$.

$r = r^* + IP + MRP = 3\% + 3\% + 0 = 6\%$

The yield on the two-year Treasury security is 6%.

Work upwards from net income.

$EBT = \frac{NI}{1-T} = \frac{1.8}{0.6} = 3.0 \text{ million}$

$EBIT = EBT + \text{Interest} = 3.0 + 2.0 = 5.0 \text{ million}$

$EBITDA - D\&A = EBIT \Rightarrow D\&A = 7.5 - 5.0 = \text{Rs } 2.5 \text{ million}$

(a) For a zero coupon bond, $P = \dfrac{M}{(1+YTM)^n}$:

$YTM = \left(\frac{1000}{400}\right)^{1/8} - 1 = 2.5^{0.125} - 1 = 12.14\%$

(b) For a perpetual bond, $P = \dfrac{C}{YTM}$. The coupon is $0.15 \times 1000 = \text{Rs } 150$.

$YTM = \frac{150}{900} = 16.67\%$

$D_0 = 8$, so $D_1 = 8(1.10) = \text{Rs } 8.80$.

(a) Expected return:

$k = \frac{D_1}{P_0} + g = \frac{8.80}{176} + 0.10 = 0.05 + 0.10 = 15\%$

(b) Value at a required return of 14%:

$P_0 = \frac{D_1}{k-g} = \frac{8.80}{0.14-0.10} = \text{Rs } 220$

(c) Yes, invest. The intrinsic value (Rs 220) is greater than the market price (Rs 176), and the expected return (15%) is greater than the required return (14%), so the stock is undervalued.

Effective annual rate:

$EAR = \left(1+\frac{APR}{m}\right)^m - 1$

Daily compounding ($m = 365$):

$EAR = \left(1+\frac{0.195}{365}\right)^{365} - 1 = 21.52\%$

Monthly compounding ($m = 12$):

$EAR = \left(1+\frac{0.195}{12}\right)^{12} - 1 = (1.01625)^{12} - 1 = 21.34\%$

The statement of cash flows reports the cash inflows and outflows of a firm during a period and explains the change in the cash balance between two balance sheet dates. It shows how the firm generated cash and how it used it, which is something the income statement (accrual basis) does not show.

It has four sections:

1. Operating activities: cash generated by the normal business, starting from net income, adding back non-cash items such as depreciation and adjusting for changes in current assets and current liabilities (receivables, inventory, payables).
2. Investing activities: cash spent on or received from the purchase and sale of long-term assets such as plant, equipment, land and long-term investments.
3. Financing activities: cash flows from raising and repaying capital, such as issue of shares and debt, repayment of loans and payment of dividends.
4. Net change in cash and reconciliation: the sum of the three activity totals gives the net increase or decrease in cash, which is added to the opening cash to get the closing cash balance shown on the balance sheet.

Taking accounts payable and accrued expenses as the current liabilities (Rs 100,000), and deferred taxes, debenture and long-term loan as long-term liabilities.

Current assets $= 50{,}000 + 100{,}000 + 400{,}000 = \text{Rs } 550{,}000$. Total debt $= 50{,}000 \times 4 + 150{,}000 = \text{Rs } 350{,}000$. Total equity $= 500{,}000 + 150{,}000 = \text{Rs } 650{,}000$.

(a) Current ratio

$\frac{550{,}000}{100{,}000} = 5.5 \text{ times}$

(b) Quick ratio

$\frac{550{,}000 - 400{,}000}{100{,}000} = 1.5 \text{ times}$

(c) Debt ratio

$\frac{350{,}000}{1{,}000{,}000} = 0.35 = 35\%$

(d) Debt-equity ratio

$\frac{350{,}000}{650{,}000} = 0.538 \text{ times}$

(e) Equity multiplier

$\frac{1{,}000{,}000}{650{,}000} = 1.538 \text{ times}$

(f) Long-term debt to total assets (debenture + long-term loan $= 200{,}000$)

$\frac{200{,}000}{1{,}000{,}000} = 20\%$

(a) The deposit must equal the present value of an ordinary annuity of Rs 10,000 for 4 years at 7%:

$PV = 10{,}000 \times \frac{1-(1.07)^{-4}}{0.07} = 10{,}000 \times 3.3872 = \text{Rs } 33{,}872.11$

(b) Immediately after the first withdrawal (end of year 1):

$33{,}872.11 \times 1.07 - 10{,}000 = 36{,}243.16 - 10{,}000 = \text{Rs } 26{,}243.16$

Check: the remaining 3 payments are worth $10{,}000 \times 2.6243 = \text{Rs } 26{,}243$.

Portfolio return

$E(R_p) = 0.6(10\%) + 0.4(6\%) = 6.0\% + 2.4\% = 8.4\%$

Portfolio risk

$\sigma_p^2 = w_X^2\sigma_X^2 + w_Y^2\sigma_Y^2 + 2w_Xw_Y\rho_{XY}\sigma_X\sigma_Y$

$\sigma_p^2 = (0.6)^2(5)^2 + (0.4)^2(4)^2 + 2(0.6)(0.4)(-0.35)(5)(4)$

$\sigma_p^2 = 9 + 2.56 - 3.36 = 8.20$

$\sigma_p = \sqrt{8.20} = 2.86\%$

The portfolio has an expected return of 8.4% with a standard deviation of about 2.86%, lower than either stock alone because of the negative correlation.

(a) After-tax cost of debt of the zero-coupon bond

Pre-tax cost (yield to maturity):

$k_d = \left(\frac{1000}{500}\right)^{1/10} - 1 = 2^{0.1} - 1 = 7.18\%$

$k_d(1-T) = 7.18\% \times (1-0.40) = 4.31\%$

(b)

a. Cost of retained earnings

$k_s = \frac{D_1}{P_0} + g = \frac{3.18}{36} + 0.06 = 8.83\% + 6\% = 14.83\%$

b. Flotation cost percentage

$F = \frac{36 - 32.40}{36} = \frac{3.60}{36} = 10\%$

c. Cost of new common stock

$k_e = \frac{D_1}{P_0(1-F)} + g = \frac{3.18}{32.40} + 0.06 = 9.81\% + 6\% = 15.81\%$

(a) Balance sheet

A balance sheet is a financial statement that shows the financial position of a firm at a particular date. It lists what the firm owns (assets), what it owes (liabilities) and the owners' claim (equity), following the equation:

$\text{Assets} = \text{Liabilities} + \text{Owners' equity}$

It provides information about:

• the types and amounts of assets (current and fixed) and their liquidity;
• the sources of financing, that is the mix of debt and equity (capital structure);
• the firm's short-term solvency (working capital) and long-term solvency;
• retained earnings and the book value of equity, which are used in ratio analysis and by lenders and investors to judge the firm's strength.

(b) Horleri Company (Rs million)

i. Net income

ii. Net cash flow $= NI + \text{Depreciation} = 2.4 + 1.0 = \text{Rs } 3.4$ million.

iii. NOPAT

$NOPAT = EBIT(1-T) = 5.0(0.6) = \text{Rs } 3.0 \text{ million}$

iv. Operating cash flow

$OCF = NOPAT + \text{Depreciation} = 3.0 + 1.0 = \text{Rs } 4.0 \text{ million}$

v. Free cash flow

Operating capital this year $= (14 - 4) + 15 = \text{Rs } 25$ million.

$\text{Net investment in operating capital} = 25 - 24 = 1.0$

$FCF = NOPAT - \text{Net investment} = 3.0 - 1.0 = \text{Rs } 2.0 \text{ million}$

Equivalent check: $OCF - \text{gross investment} = 4.0 - (1.0+1.0) = 2.0$.

vi. Economic Value Added

$EVA = NOPAT - (\text{Cost of capital} \times \text{Operating capital}) = 3.0 - 0.10(25) = \text{Rs } 0.5 \text{ million}$

Financial markets are markets in which funds are transferred from savers (surplus units) to borrowers (deficit units) through the buying and selling of financial assets such as shares, bonds and treasury bills. They include the money market and the capital market.

The liquidity position is measured by the firm's ability to meet short-term obligations, using:

• Current ratio $= \dfrac{\text{Current assets}}{\text{Current liabilities}}$
• Quick (acid-test) ratio $= \dfrac{\text{Current assets} - \text{Inventory}}{\text{Current liabilities}}$

The higher the ratios, the stronger the liquidity. Net working capital (current assets minus current liabilities) is also used.

A financial statement is a formal report that summarises the financial activities and position of a firm for a period. The main statements are the balance sheet, income statement, statement of retained earnings (changes in equity) and statement of cash flows. They are used by managers, investors and creditors to judge performance and take decisions.

$r = r^* + IP + MRP = 4\% + 8\% + 2\% = 14\%$

The yield on the 5-year security is 14%.

A preferred stock pays a fixed dividend forever, so it is valued as a perpetuity:

$V = \frac{D}{k_p} = \frac{15}{0.12} = \text{Rs } 125$

$EAR = (1+0.03)^{12} - 1 = 1.4258 - 1 = 42.58\%$

The effective annual interest rate is about 42.58% (the nominal rate is 36%).

The cash conversion cycle (CCC) is the time between paying for inventory and collecting cash from customers. A longer CCC means cash is tied up in inventory and receivables for more days, so the firm needs more working capital (financing) to support operations. A shorter CCC reduces the working capital required.

$CCC = ICP + RCP - PDP$

Interest on debt is tax-deductible, so the firm's actual cost is less than the interest rate paid. The tax saving reduces the cost:

$k_d(\text{after tax}) = k_d(1-T)$

Since the shareholders' return is calculated after tax, and the cost of equity and preferred stock is on an after-tax basis, debt cost must also be after tax to be comparable and to compute the correct WACC.

$PV = \frac{FV}{(1+r)^n} = \frac{10{,}500}{(1.08)^5} = \frac{10{,}500}{1.4693} = \text{Rs } 7{,}146.12$

Finance functions are the decisions that a financial manager has to take to achieve the firm's goal of maximising shareholders' wealth. The main functions are:

1. Investment (capital budgeting) decision: deciding which long-term assets and projects to invest in, based on expected returns and risk. It also includes working capital (current asset) management.
2. Financing (capital structure) decision: deciding the sources of funds and the best mix of debt and equity so that the cost of capital is minimised and value maximised.
3. Dividend decision: deciding how much of the profit to pay as dividends and how much to retain for reinvestment.
4. Liquidity (working capital) management: ensuring that the firm has enough cash to meet its day-to-day obligations without keeping idle funds.
5. Financial analysis, planning and control: analysing financial statements, forecasting funds needs, preparing budgets and controlling performance.
6. Risk management: identifying and managing financial risks, for example through insurance and hedging.

The market interest rate (nominal rate) on a security is made up of a real risk-free rate and several premiums:

$k = k^* + IP + DRP + LP + MRP$

• Real risk-free rate ($k^*$): the rate on a risk-free security if no inflation is expected; it depends on the savings of households and the investment opportunities (productivity) of firms.
• Inflation premium (IP): compensation to lenders for the expected loss of purchasing power; it equals the average expected inflation over the life of the security.
• Default risk premium (DRP): compensation for the risk that the borrower will not pay interest or principal in full; it is zero for government securities and rises as credit quality falls.
• Liquidity premium (LP): extra yield on securities which cannot be sold quickly at a fair price.
• Maturity risk premium (MRP): extra yield for long-term securities, which are exposed to greater interest rate risk than short-term ones.

Other factors such as monetary policy, the government's budget deficit and the level of economic activity also affect these components.

Yes, I agree. Common stocks are generally riskier than bonds, for these reasons:

• Income is uncertain: bondholders get fixed interest and the principal at maturity, but dividends on common stock are not promised and are paid only after all other claims.
• Residual claim: in liquidation, bondholders are paid before preferred and common shareholders, who get what is left, if anything.
• Price volatility: the price of common stock depends on earnings, growth and market sentiment and fluctuates much more than bond prices, which are tied to a fixed cash flow.
• No maturity date: there is no fixed date at which the investor is repaid the principal.

Because of the higher risk, investors demand a higher expected return on common stocks than on bonds (the equity risk premium). The reward for this risk is the potential for capital gains and growing dividends.

(a) Operating cycle and cash conversion cycle

$\text{Operating cycle} = ICP + RCP = 35 + 30 = 65 \text{ days}$

$CCC = \text{Operating cycle} - PDP = 65 - 25 = 40 \text{ days}$

(b) Financing required

$\text{Daily investment} = \frac{6{,}000{,}000}{360} = \text{Rs } 16{,}666.67$

$\text{Financing} = 40 \times 16{,}666.67 = \text{Rs } 666{,}667$

(c) Ways to reduce the CCC

• Reduce the inventory conversion period by better inventory management (for example just-in-time) and faster production and sales.
• Reduce the receivables collection period by tighter credit policy, discounts for early payment and stricter collection.
• Increase the payables deferral period by negotiating longer credit from suppliers, without losing discounts or goodwill.

Semiannual payments: $n = 7 \times 2 = 14$, coupon $= 1000 \times 10\%/2 = \text{Rs } 50$, and $r = 12\%/2 = 6\%$.

$V = 50 \times \frac{1-(1.06)^{-14}}{0.06} + \frac{1000}{(1.06)^{14}}$

$V = 50(9.2950) + 1000(0.4423) = 464.75 + 442.30 = \text{Rs } 907.05$

The bond is worth about Rs 907.05 (it sells at a discount because the required return exceeds the coupon rate).

(a) Annual payment

$PMT = \frac{PV}{\frac{1-(1+r)^{-n}}{r}} = \frac{100{,}000}{2.48685} = \text{Rs } 40{,}211.48$

(b) Loan amortization schedule

Last dividend $D_0 = 24$, $P_0 = 360$, $k = 12\%$.

Growth rate

$P_0 = \frac{D_0(1+g)}{k-g} \Rightarrow 360(0.12-g) = 24(1+g)$

$43.2 - 360g = 24 + 24g \Rightarrow 19.2 = 384g \Rightarrow g = 5\%$

Price after 3 years

With constant growth the price also grows at $g$:

$P_3 = P_0(1+g)^3 = 360(1.05)^3 = \text{Rs } 416.75$

Check: $D_4 = 24(1.05)^4 = 29.17$ and $P_3 = 29.17/(0.12-0.05) = 416.7$.

Financial environment means the set of institutions, markets, instruments and rules, together with the economic and legal conditions, within which a firm raises and uses funds. It decides the sources, cost and availability of finance, and so affects financial decisions.

Major components

1. Financial markets: places where funds flow from savers to borrowers. The money market deals in short-term (up to one year) instruments such as treasury bills, commercial paper and certificates of deposit; the capital market deals in long-term securities such as shares and bonds. Markets are also divided into primary and secondary markets.
2. Financial institutions: intermediaries that collect savings and lend them. These include commercial banks, development banks, finance companies, insurance companies, pension and provident funds (such as the Employees Provident Fund and Citizen Investment Trust) and mutual funds.
3. Financial instruments (securities): the claims traded, such as shares, bonds, debentures, treasury bills, deposits and derivatives.
4. Regulatory bodies: institutions which regulate and supervise the system, for example the central bank (Nepal Rastra Bank), the Securities Board of Nepal, the stock exchange (NEPSE) and the Insurance Authority.
5. Interest rates and the economic environment: the price of funds (interest rate) and conditions such as inflation, monetary and fiscal policy and the business cycle, which affect the cost and availability of capital.
6. Taxation and legal environment: tax laws, company law and securities law which affect the cost and form of finance and investor protection.

A sound financial environment encourages savings and investment and lets firms raise funds at lower cost.

(a) Semiannual deposits: $n = 5 \times 2 = 10$, $i = 12\%/2 = 6\%$.

$FVA = 400 \times \frac{(1.06)^{10}-1}{0.06} = 400 \times 13.1808 = \text{Rs } 5{,}272.32$

(b) Quarterly deposits: $n = 5 \times 4 = 20$, $i = 12\%/4 = 3\%$.

$FVA = 200 \times \frac{(1.03)^{20}-1}{0.03} = 200 \times 26.8704 = \text{Rs } 5{,}374.07$

(c) Both annuities deposit Rs 4,000 in total (Rs 400 $\times$ 10 and Rs 200 $\times$ 20) at the same nominal rate of 12%. Annuity (b) is larger for two reasons:

• Quarterly compounding gives a higher effective annual rate, $(1.03)^4 - 1 = 12.55\%$, than semiannual compounding, $(1.06)^2 - 1 = 12.36\%$, so interest is earned on interest more often.
• Each Rs 200 is deposited earlier than the Rs 400 payments (half of each semiannual amount is deposited three months sooner), so it earns interest for longer.

Therefore the more frequent the compounding and deposits, the larger the terminal value.

(a) Equity needed to keep the capital structure

The weights are debt 40%, preferred 10% and equity 50%.

$\text{Equity} = 0.50 \times 50 \text{ million} = \text{Rs } 25 \text{ million}$

(b) Equity from new stock

The problem gives no retained earnings figure for the year, so the whole equity requirement is taken as being raised from new stock, if retained earnings are not available. If retained earnings are available, the new stock is the equity required (Rs 25 million) less the retained earnings available. For part (e) the full Rs 25 million is taken as new stock.

(c) Component costs

1. New debt

Net proceeds $= 970 - 0.02(1000) = \text{Rs } 950$. Annual interest $= \text{Rs } 90$.

Approximate yield to maturity on net proceeds:

$k_d = \frac{90 + \frac{1000-950}{10}}{\frac{1000+950}{2}} = \frac{95}{975} = 9.74\%$

$k_d(1-T) = 9.74\% \times 0.6 = 5.85\%$

2. New preferred stock

Net proceeds $= 95 - 5 = \text{Rs } 90$. Dividend $= 12\% \times 100 = \text{Rs } 12$.

$k_p = \frac{12}{90} = 13.33\%$

3. Retained earnings (internal equity)

$k_s = \frac{D_1}{P_0} + g = \frac{50}{500} + 0.06 = 16\%$

4. New common equity

Net proceeds $= 440 - 20 = \text{Rs } 420$.

$k_e = \frac{50}{420} + 0.06 = 11.90\% + 6\% = 17.90\%$

(d) WACC using only retained earnings

(e) WACC when Rs 50 million is raised

All the equity (Rs 25 million) comes from new common stock:

(f) Uses of WACC

• It is the discount rate for capital budgeting: projects whose return exceeds the WACC (NPV positive) add value.
• It is the hurdle rate used to accept or reject investment proposals.
• It is used to evaluate capital structure choices; the structure with the lowest WACC maximises firm value.
• It is used in valuing the firm by discounting free cash flows, and in measuring performance (EVA).
• It guides financing decisions on how to raise funds at the lowest overall cost.

Finance is the art and science of managing money. It deals with the acquisition of funds (financing), their investment in assets (investing) and the management of the firm's cash and resources so as to maximise value.

A treasury bill (T-bill) is a short-term government security, with maturity up to one year (in Nepal, 28, 91, 182 or 364 days), issued at a discount to face value and redeemed at par. The difference is the investor's return. It is considered virtually risk-free.

Four types of financial statements:

1. Income statement (profit and loss account)
2. Balance sheet (statement of financial position)
3. Statement of cash flows
4. Statement of retained earnings (statement of changes in equity)

Default risk is the risk that a borrower (issuer of a bond or loan) will fail to pay the promised interest or repay the principal on time and in full. The higher the chance of default, the higher the yield investors demand; the extra return is called the default risk premium. Government securities carry almost no default risk, while low-rated corporate bonds carry high default risk.

• Annuity: a series of equal cash flows occurring at regular intervals for a fixed, limited number of periods (e.g., a 5-year loan installment of Rs 10,000 per year). Its present value is $PMT \times \frac{1-(1+r)^{-n}}{r}$.
• Perpetuity: a series of equal cash flows at regular intervals that continues forever (no end date), e.g., preferred dividends or consols. Its present value is $PV = \frac{PMT}{r}$.

Thus the difference is that an annuity has a finite life while a perpetuity has an infinite life.

Dividend yield is the annual dividend per share expressed as a percentage of the current market price:

$\text{Dividend yield} = \frac{D_1}{P_0}$

Illustration: if a share sells at Rs 200 and is expected to pay an annual dividend of Rs 12, then

$\text{Dividend yield} = \frac{12}{200} = 6\%$

Example: a Rs 1,000 bond with a 12% coupon when the market rate is 10% sells at a premium; with an 8% coupon it sells at a discount.

The normal (constant) growth model of the dividend discount model assumes that dividends grow at a constant rate $g$ forever, with $g$ less than the required return $k_e$. Hence

$P_0 = \frac{D_0(1+g)}{k_e - g} = \frac{D_1}{k_e-g}$

Dividends are therefore assumed to grow at a stable, perpetual rate that does not change over time.

The inventory conversion period is the average time needed to convert raw materials into finished goods and sell them. It is a part of the operating cycle. A longer inventory conversion period means funds remain tied up in stock for more days, which lengthens the operating/cash conversion cycle and increases the working capital required. A shorter period (faster inventory turnover) releases funds and reduces working capital needs. Working capital is directly proportional to the inventory period.

Effective annual rate with quarterly compounding ($m = 4$):

$EAR = \left(1+\frac{0.08}{4}\right)^4 - 1 = (1.02)^4 - 1 = 1.082432 - 1 = 0.0824$

Effective rate = 8.24% per year.

Financial institutions are organizations that act as intermediaries in the financial system. They collect funds from savers and surplus units and channel them to borrowers and investors, and they provide services such as payments, insurance, investment and advisory. Examples are commercial banks, finance companies, insurance companies, cooperatives and mutual funds.

Depository vs non-depository institutions

The cost of capital is the minimum rate of return a firm must earn on its investments to satisfy its investors (lenders and owners). It is widely applied in financial decision making:

1. Capital budgeting: it is the discount rate (hurdle rate) used to compute NPV and the benchmark for IRR. A project is accepted if NPV > 0, or IRR > cost of capital.
2. Capital structure decisions: the firm aims for the mix of debt and equity that minimises the weighted average cost of capital (WACC) and so maximises firm value.
3. Valuation of the firm: firm value is the present value of future cash flows discounted at WACC; a lower WACC raises value.
4. Dividend policy: the cost of retained earnings (opportunity cost to shareholders) helps decide whether to retain profits or pay dividends.
5. Financing and leasing decisions: it is used to compare sources of funds, and to evaluate lease versus buy and refunding of debt.
6. Performance evaluation: returns on divisions or projects are compared with the cost of capital (e.g., economic value added).

Concept: Working capital is the funds invested in a firm's short-term (current) assets such as cash, receivables and inventory.

• Gross working capital = total current assets.
• Net working capital (NWC) = current assets - current liabilities. It shows the part of current assets financed by long-term funds.

Working capital management aims to maintain enough liquidity to meet day-to-day operations without holding excess idle funds.

Types of working capital

On the basis of concept:

1. Gross working capital: total current assets.
2. Net working capital: current assets minus current liabilities.

On the basis of time:

1. Permanent (fixed) working capital: the minimum level of current assets needed at all times to carry on business, even in the slackest period.
2. Temporary (variable) working capital: the extra current assets needed due to seasonal or special demands; it fluctuates with business activity. It includes seasonal and special working capital.

Other types: Negative working capital arises when current liabilities exceed current assets.

$FV = PV(1+r)^n$ with $r = 10\%$, end of year 5.

(a) Rs 500,000 deposited now (5 years):

$FV = 500{,}000(1.10)^5 = 500{,}000 \times 1.61051 = \text{Rs } 805{,}255$

(b) Rs 800,000 deposited at end of year 2 (3 years remain):

$FV = 800{,}000(1.10)^3 = 800{,}000 \times 1.331 = \text{Rs } 1{,}064{,}800$

(c) Rs 100,000 at the end of each year for 5 years (ordinary annuity):

$FVA = 100{,}000 \times \frac{(1.10)^5-1}{0.10} = 100{,}000 \times 6.1051 = \text{Rs } 610{,}510$

Total value at the end of year 5 if all three are considered together = 805,255 + 1,064,800 + 610,510 = Rs 2,480,565.

$V = \sum \frac{C}{(1+k_d)^t} + \frac{M}{(1+k_d)^n}$, with required rate $k_d = 10\%$.

(a) No maturity is given, so the bond is treated as a perpetual bond. Annual coupon = $0.09 \times 1000 = \text{Rs } 90$.

$V = \frac{90}{0.10} = \text{Rs } 900$

It sells at a discount because the coupon (9%) is below the required rate (10%).

(b) Zero coupon bond, 7 years:

$V = \frac{1000}{(1.10)^7} = \frac{1000}{1.9487} = \text{Rs } 513.16$

(c) Coupon = Rs 120, $n = 10$:

$V = 120 \times \frac{1-(1.10)^{-10}}{0.10} + \frac{1000}{(1.10)^{10}}$

$V = 120 \times 6.1446 + 1000 \times 0.3855 = 737.35 + 385.54 = \text{Rs } 1{,}122.89$

It sells at a premium because the coupon (12%) exceeds the required rate (10%).

Given: $P_0 = 210$, $D_0 = 20$, $g = 5\%$.

$D_1 = D_0(1+g) = 20 \times 1.05 = \text{Rs } 21$

Required rate of return:

$k_e = \frac{D_1}{P_0} + g = \frac{21}{210} + 0.05 = 0.10 + 0.05 = 15\%$

Expected price one year from today: price grows at 5%, so

$P_1 = \frac{D_2}{k_e - g} = \frac{21 \times 1.05}{0.15-0.05} = \frac{22.05}{0.10} = \text{Rs } 220.50$

(Equivalently $210 \times 1.05 = 220.50$.)

(a)

Inventory conversion period (ICP) = $\frac{360}{8} = 45$ days

Receivable collection period (RCP) = 60 days

Payables deferral period (PDP) = 35 days

$\text{Operating cycle} = ICP + RCP = 45 + 60 = \mathbf{105\ days}$

$\text{Cash conversion cycle} = OC - PDP = 105 - 35 = \mathbf{70\ days}$

(b) The annual operating investment is Rs 3,500,000.

$\text{Daily cash operating expenses} = \frac{3{,}500{,}000}{360} = \text{Rs } 9{,}722.22$

Negotiated financing required to support the cash conversion cycle:

$9{,}722.22 \times 70 = \text{Rs } 680{,}555.56 \approx \text{Rs } 680{,}556$

Financial goal of the firm

The primary financial goal of a firm is shareholder wealth maximization, i.e., maximizing the market value (price per share) of the existing owners' common stock. Financial decisions (investment, financing and dividend) are judged by whether they increase the market price of the firm's shares. Profit maximization is an older and narrower goal; wealth maximization is considered superior.

$\text{Wealth} = \text{PV of expected future cash flows to owners} = \sum_{t=1}^{\infty}\frac{CF_t}{(1+k)^t}$

Key features

1. Based on cash flows, not accounting profit: it considers actual cash flows, which cannot be easily manipulated by accounting methods.
2. Considers the time value of money: future cash flows are discounted to present value, so earlier cash flows are worth more.
3. Considers risk: the discount rate reflects the riskiness of cash flows; riskier projects must give higher returns.
4. Long-term perspective: it looks at the whole life of the firm rather than only the current year's earnings.
5. Considers dividend and timing: the size, timing and certainty of returns to shareholders are taken into account.
6. Measurable: the market price of shares gives a clear, objective measure of success.
7. Serves all stakeholders: a firm can increase share value only by satisfying customers, employees, creditors and society, so the interests of other stakeholders are indirectly protected.
8. Agency issue: managers (agents) may pursue their own interests, so the goal requires monitoring and incentives such as stock options and sound corporate governance.

Why preferred over profit maximization: profit maximization ignores timing, risk and the quality of earnings, and can be manipulated; wealth maximization avoids these weaknesses.

Interest rate = real risk-free rate ($r^*$) + expected inflation (IP) + maturity risk premium (MRP) + other premiums. Here $r^* = 2\%$ and MRP = 0 for bonds of 5 years or less.

(a) Average expected inflation over the next 4 years (2025-2028):

$\frac{5+6+7+8}{4} = \frac{26}{4} = \mathbf{6.5\%}$

(b) Interest rate on 4-year T-bonds:

$r = r^* + IP = 2\% + 6.5\% = \mathbf{8.5\%}$

(c) For the 5-year bond, $9\% = 2\% + IP_5$, so the average inflation over 5 years is 7%.

$\text{Total inflation over 5 years} = 7\% \times 5 = 35\%$

$\text{Inflation in 2029} = 35 - 26 = \mathbf{9\%}$

(d) Maturity risk premium is the extra yield investors demand for the greater price (interest rate) risk of longer-term bonds, because a rise in interest rates causes bigger price falls for long-maturity bonds. Hence the longer the maturity, the higher the MRP and the higher the interest rate on the bond. It makes the yield curve upward sloping, other things being equal.

Loan = Rs 300,000, $r = 12\%$, $n = 3$ years.

(a) Annual payment:

$PMT = \frac{300{,}000}{\frac{1-(1.12)^{-3}}{0.12}} = \frac{300{,}000}{2.4018} = \text{Rs } 124{,}904.69 \approx \text{Rs } 124{,}905$

(b) Amortization schedule (Rs):

(c) Monthly payments: $i = 12\%/12 = 1\%$ per month, $n = 3 \times 12 = 36$.

$EMI = \frac{300{,}000}{\frac{1-(1.01)^{-36}}{0.01}} = \frac{300{,}000}{30.1075} = \text{Rs } 9{,}964.29$

(a) Component costs

Debt (after tax):

$k_d = 10\%(1-0.30) = \mathbf{7.0\%}$

Preferred stock:

$k_p = \frac{D_p}{P_n} = \frac{9}{100-6} = \frac{9}{94} = \mathbf{9.57\%}$

Retained earnings: $D_1 = 20 \times 1.04 = 20.80$

$k_r = \frac{D_1}{P_0} + g = \frac{20.80}{208} + 0.04 = 0.10 + 0.04 = \mathbf{14.0\%}$

New common stock (flotation cost 5%):

$k_e = \frac{D_1}{P_0(1-F)} + g = \frac{20.80}{208(0.95)} + 0.04 = \frac{20.80}{197.60} + 0.04 = 0.1053 + 0.04 = \mathbf{14.53\%}$

(b) WACC (common equity from retained earnings, $k_r = 14\%$):

(a) Liquidity (2025E)

$\text{Current ratio} = \frac{2{,}680{,}112}{1{,}039{,}800} = 2.58$

$\text{Quick ratio} = \frac{2{,}680{,}112 - 1{,}716{,}480}{1{,}039{,}800} = \frac{963{,}632}{1{,}039{,}800} = 0.93$